Related papers: Enumeration and Decidable Properties of Automatic …
We obtain an index of the complexity of a random sequence by allowing the role of the measure in classical probability theory to be played by a function we call the generating mechanism. Typically, this generating mechanism will be a finite…
Let $n$ and $k$ be positive integers, and let $F$ be an alphabet of size $n$. A sequence over $F$ of length $m$ is a \emph{$k$-radius sequence} if any two distinct elements of $F$ occur within distance $k$ of each other somewhere in the…
Parameterized quantum circuits are the core of new technologies such as variational quantum algorithms and quantum machine learning, which makes studying its properties a valuable task. We implement parameterized circuits with definite and…
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by…
Following up on a paper of Balamohan, Kuznetsov, and Tanny, we analyze a variant of Hofstadter's Q-sequence and show it is 2-automatic. An automaton computing the sequence is explicitly given.
In this note, we consider the problem of generating $k$-factorable graphic sequences with connected (resp. no connected) $k$-factors.
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
Instruction sequence is a key concept in practice, but it has as yet not come prominently into the picture in theoretical circles. This paper concerns instruction sequences, the behaviours produced by them under execution, the interaction…
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such that there is no minimal deterministic finite automaton with…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
We introduce the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence, and we prove a variant of Cobham's theorem for the newly introduced class of sequences.
In this article we consider the completely multiplicative sequences $(a_n)_{n \in \mathbf{N}}$ defined on a field $\mathbf{K}$ and satisfying $$\sum_{p| p \leq n, a_p \neq 1, p \in \mathbf{P}}\frac{1}{p}<\infty,$$ where $\mathbf{P}$ is the…
Sequence classification is the task of predicting a class label given a sequence of observations. In many applications such as healthcare monitoring or intrusion detection, early classification is crucial to prompt intervention. In this…
This study applies the binomial, k-binomial, rising k-binomial and falling k-binomial transforms to the modified k-Fibonacci-like sequence. Also, the Binet formulas and generating functions of the above mentioned four transforms are newly…
A tree automatic structure is a structure whose domain can be encoded by a regular tree language such that each relation is recognisable by a finite automaton processing tuples of trees synchronously. Words can be regarded as specific…
A k-digraph is an orientation of a multi-graph that is without loops and contains at most k edges between any pair of distinct vertices. We obtain necessary and sufficient conditions for a sequence of non-negative integers in non-decreasing…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two…
We prove sharp limit theorems on random walks on graphs with values in finite groups. We then apply these results (together with some elementary algebraic geometry, number theory, and representation theory) to finite quotients of lattices…
The classes of depth-bounded and name-bounded processes are fragments of the pi-calculus for which some of the decision problems that are undecidable for the full calculus become decidable. P is depth-bounded at level k if every reduction…